Blackboard Math™ Arithmetic

Practice arithmetic just like Abe Lincoln. Updated for the 21st century.

Blackboard Math™ Arithmetic is the ONLY tablet-native app that uses the entire touch-screen as a virtual slate for children to solve math problems longhand.

It is not another cell phone app with scaled up graphics to fill out a larger display. It is not another arcade-style game with distracting graphics, and limited to simple mental math and multiple-choice answers. It won’t indulge a short attention-span or exacerbate ADHD tendencies. Rather, it is a modern take on the traditional method of learning math: careful practice and working out problems longhand.

Blackboard Math™ follows the adage, “if you want to remember something write it down.” Blackboard Math™ has students writing down their work as they go about solving complex, multi-digit arithmetic problems longhand.

The benefits of solving math problems longhand are multifold:

Improves learning by involving the fine motor control centers of the brain

Exercises the full range of steps required to solve arithmetic problems

Makes complicated problems more solvable

Rewards focus, care, and contentiousness, over rapid-fire answers and guess-work

Promotes attention-span

Creates a written record to review potential sources of repeat mistakes

Additionally, Blackboard Math™ saves students’ work so parents can review it later. Parents are free to be coaches and mentors, while the app itself does the rote work of generating problems and grading answers. Also, Blackboard Math™ tracks how long and how often your child uses the app. Parents can be assured their child is making an effort on their math practice.

Frequently Asked Questions and Future Development

Can the app read my hand-writing for the answer?

That would be so awesome. Alas, it cannot. It’s certainly something we’ve thought of. Everyone that uses the app wishes for it, but obviously hand-writing recognition is a hard problem. Harder still with young children. We’d like to get to it some day, but it’s not on any defined time-frame.

I pick Intermediate or Expert difficulty, but still get asked easy questions like 230 * 1.

At this time the difficulty choices are only a short-cut for selecting the magnitudes of the numbers in the problem questions. Each digit in the problem is randomly generated with no consideration that 0′s, 1′s, and 2′s are generally pretty easy, while 7′s, 8′s and 9′s are generally hard. The app makes some adjustment for leading 0′s, and for 0′s and 1′s in multiplication and division, but that is the extent of the filtering. Adding an active AI to learn what the student knows and dynamically choose problems appropriate for their skill level is near the top of our to-do list. In the future, we’d like to have the difficulty choices create a weighted value for generating digits instead of all being equally probable, as is the case with randomly generated numbers. We hope to have a weighted-probability number generator some time in 2014. If it’s a concern, please be assured buying now will entitle you to all future updates. In fact, buying now sends us the message that our users care and want to see us continue on its development.

Why doesn’t division have remainders or decimals?

In fact, we added remainders to the full version of the app for release v1.2. If you do not see a selection for ‘Allow Remainder Answers’ in the session set-up activity, check whether you have downloaded the latest release. Also, we have a separate app that is dedicated to decimal arithmetic. Please take a look at it and tell us what you think.

How do I erase mistakes?

Open the “Chalk Tray” by tapping the chalk & eraser icon in the top-right section in the Android Action Bar. From it you can choose the sponge and bucket which will “wash” the entire blackboard allowing you to start over, or you can choose the eraser and spot erase just the one or two numbers where you may have made a mistake. The spot eraser is handy with multi-digit multiplication and division. With addition and subtraction it’s often faster and easier to just wash everything and start over. (Note, the action bar was added in version 2.0. Prior to that, the chalk tray was opened by double-tapping on the screen. If you don’t have an action bar in your app, you are still running an older version of Blackboard Math, go to the app market you originally purchased it from and download the latest version. Updates are always free.)

How are the scores determined?

The scoring algorithm might be something only an engineer could love. It is tuned to reward difficulty over speed. The more digits in the operands, the more points awarded for a correct answer. Also, we do respect quick answers and the proficiency that is required to deliver them. A bonus factor of 20 to 100% is given for answers delivered within the proficient time limit. The threshold increases with the difficulty, while the bonus factor decreases. The presumption is that simple, mental-math problems should be answered proficiently and deserve a large relative bonus, while difficult answers that need to be computed longhand have most of their value in the base point value. Answering a difficult problem quickly is nice, but not the point of working a difficult problem. Finally, it must be said that we did not spend considerable time optimizing the proficiency thresholds for the more difficult problem settings, especially 3 and 4 digit multiplication and division. This is high on our list to revisit. Until then, please realize the score is more a relative measure of the child’s improvement over time, than an absolute assessment of skill.

What are the meanings of the various faces in the session review?

The faces are intended to give a quick and fun overview for how a practice session went.

The green, open-mouth smile means the answer was correct and within the time limit deemed for proficiency.

The green, closed-mouth smile means the answer was correct, but it took longer than the proficiency time limit. The proficiency thresholds are reliable for the 1 and 2 digit numbers, but still need some tuning for the 3 and 4 digit numbers. Don’t read too much into these differences on the larger numbers.

The orange face means the first answer was wrong, but was resubmitted correctly the second time.

The red face means both attempts were incorrect and the app gave the student the correct answer.

I am using the app with twins. Is there a way for me to track their practices separately?

We are glad you asked. As of version 2.0, released in September 2013, we have added support for multi-user sign-in. This allows you to create up to 4 student profiles in addition to the default Guest account. The Guest account is intended for demonstration purposes by parents and teachers so as not to interfere with the history, scoring, or settings of the student users. If you are upgrading from an earlier version, the practice history and settings will be imported and saved in the default Guest account. You can then rename the Guest account to store those into a dedicated student profile. To rename the Guest, or any profile, tap the edit profile icon on the lower right of the sign-in window, then tap on the profile you wish to rename. Since renaming the Guest account effectively creates a new student profile, the Guest cannot be renamed if there are already four student profiles active. A student profile will have to be deleted first. Educators who need more than four student profiles should please contact us at support@edisongauss.com for our special classroom edition.

Finally, for convenience to users that are using the app with a single student, the app will skip the Sign-in screen and automatically select the student profile if there is one and only one custom profile in existence. You can still return to the Sign-in screen after the auto-login has occurred by tapping the back arrow from the Welcome screen.

If you have any questions not addressed in this section please drop us a line. We have a long list of features we want to add. Scheduling and prioritizing them will depend in no small amount on our customers’ comments and feedback. We want to hear from you and greatly appreciate any input you might wish to share. If you enjoy our app and want to see us do more like it, after purchasing it, you can help us most by writing a positive review in the marketplace from which you bought it. Also, recommending us to any friends you may know whom own tablets is a great help. There is an ocean of apps out there and rising above the surf to get noticed by customers in the first place is the hardest part.

A not so brief statement about the competition.

If kids find them interesting, we have no problem with them playing many of the various math games that are out there. However, we take exception with a few of the typical elements in many math games.

First is what engineers call duty-cycle, or the amount of time the kids spend practicing math versus the amount of time they spend waiting for the various game attributes in the software to play out. Some games feel like they spend over half their time on things totally unrelated to the student practicing math. That is time not spent doing something productive. If the child has 20 minutes for a session of math practice, but 10 of it is spent watching cartoon animations and talking animals, he or she is only getting half the actual math practice that they could be getting.

Our second issue with the typical math app is simply the limited value of mental math. Math is about far more than computing the correct answer to the sum, difference, product, etc. of two numbers. Rather, math is a set of processes for breaking down a large, complex problem into smaller, more easily solved problems. The process is what is important. The rigor of thought and the understanding from visualizing how complex systems interact and change, something that only comes from putting the processes into action, is the real value of practicing math.

Another way to look at it is when we were growing up, a common refrain from teachers and parents was that you had to learn to compute arithmetic because you wouldn’t always have a calculator. The batteries could be dead. You might forget it at home. And various other reasons that I think we all have to admit seem less and less relevant as time goes on. However, that doesn’t diminish the value in being able to think in a structured and logical fashion, and being able to work through a problem, math or otherwise, from beginning to end. This is the foundation of intelligence. This, we think, is the value in learning and practicing arithmetic longhand. Also, while the value of being able to compute any arbitrary answer is far less than in generations past, the rigorous thinking that occurs to know how to compute the answers is even more valuable in today’s highly technological and abstract society. Math is exercise for the brain, and computers are no more a replacement for it than TV and movies are a replacement for reading.

What might be our biggest complaint with most of the math games that are produced is captured by the saying, “you get what you pay for.” Now, that is usually meant to disparage the false economy of cheaper alternatives compared to a name-brand product. However, it can also be used to mean that if you reward something, you are going to get more of it. In this context, rewarding fast, but shallow thinking, means the students are going to be trained as fast, but shallow thinkers. A lot of games are races against the clock to score points with the “cost” of being wrong relatively small. Not only is it a recipe for short-attention spans and exacerbated ADHD-symptoms, it is the exact opposite of real life. Real life is about taking the time necessary to get a problem solved right the first time. Also, in real life the more difficult the job, the better the pay.

On the better pay for more difficult work topic, Blackboard Math uses a multi-factor scoring system to reward difficulty over speed. As we mentioned in the Frequently Asked Questions section, the following might be something only an engineer could love. Each problem type has a base score that is dependent on the size of the numbers being computed. The base score increases greatly with the size of the numbers. Single digit addition has a base score of 4 while 4 by 4 digits addition has a base score of 24, or 6 times larger. Next, a proficiency factor is applied if the problem is answered correctly in a timely fashion. We do recognize value in prompt answers. However, the proficiency factor decreases as the numbers get larger. This means that on a relative basis, answering quickly on easy, what should be mental math, problems yields a bonus of premium of 100%, answering quickly on hard problems that need to be worked longhand regardless, yields a bonus of premium of 20% at its lowest. After an upper time limit, the proficiency factor becomes a fraction so that the students still score points, but fewer than the base amount. Lastly, in an effort to reward persistence, we use a fractional bonus factor if the answer is wrong on the first submission, but is fixed and answered correctly on the second submission. In this way, the fractional bonus factor allows the student to still score points for going back, fixing their work, and trying again.

A truly brief statement on our ad-network policy.

No Ads. Ever. Parents should have control on what their children are exposed to.
* Multi-user avatars are reproduced or modified from artwork created and shared by Neel Mehta and used according to the terms described in the Creative Commons 3.0 Attribution License.

App Start & Sign in

Sign In allows sharing of a tablet among children in a classroom or family; parents and teachers can use the dedicated Guest account to demonstrate solving problems without interfering with a student's practice history

App Start

tap one of the four icons to go to the corresponding activity

Setup

choose the operator, difficulty, magnitude of operands, and quantity of problems you wish to practice

Practice

using your finger, simply write on the screen to work out a solution; use the soft keyboard at the top to submit the answer

Practice

tap on the chalk & eraser icon in the Action Bar at the top-right to open the 'Chalk Tray' which has buttons for customizing the chalk size and color, spot erasing, "washing" the entire blackboard, and changing the blackboard background

Calendar

practice results are summarized by operator and displayed in a helpful calendar format (click to enlarge); tap on a day to open the session review